Chernobyl Control Rod Graphite "Tips"

It seems the straw that broke the camel's back at Chernobyl was the "positive SCRAM effect" caused by the graphite "tips" on the control rods. Of course they're not really tips (we'll use the term displacers going forward), as they're nearly as tall as the control rods themselves and the reactor core as a whole, with a critical 1.25M column of water above and below. There's a good diagram here: http://accidont.ru/ENG/rodes.html even though the text is poorly translated, and the Vlogbrothers also put together a great video with a similar diagram here: https://www.youtube.com/watch?v=hIGtTImeYU4 that show the position of the control rods, the displacers, and the relative neutron flux/reactivity distributed over the height of the core.

What I can't understand, not being a nuclear physicist myself is why the neutron flux went so high at the bottom of the reactor when the rods were inserted. The graphs show a huge spike in reactivity when the bottom of the displacers are aligned with the bottom of the reactor core (position "c" in the accident.ru diagram). I understand why the reactivity goes up there, because neutron-moderating graphite is replacing neutron-absorbing water, but I don't understand why the reactivity goes up apparently an order of magnitude or more compared to what, in my mind, is exactly the same condition as in the center of the reactor. I would think that it would only shift the graph shown in position "a" downward, removing the falloff at the end. Even the "bulge" at position "b" is a bit of a head-scratcher to me because for most of the height of the reactor the displacer is still in the same position it's always been.

Is this a temporal issue, where if the rod insertion was stopped at position "c" under normal circumstances, that flux spike would equalize after some period of time, perhaps even a very short time? Was steam being generated at the bottom of the reactor rather than at the top (how?), causing the positive void coefficient to become apparent here but not yet in the rest of the reactor? Is it because the xenon poisoning was concentrated in the center of the reactor (thus the slight decrease in flux shown in graph "a" at center as compared to 80% top or bottom), so the little bit of extra reactivity caused by the water displacement caused runaway reactivity due to the xenon being burned off? Help me out here. This is the one and only bit of the situation I haven't been able to wrap my head around.
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Not a reactor expert either but I think that picture is not of the reactivity of the reactor but the neutron flux.

The higher the neutron flux, the higher the increase in neutron flux in response to a small increase in reactivity.

A large contributing factor to the accident was the large axial difference in power distribution in the core at the time of the accident. Spatial power differences in a large core like RBMK were already "difficult" to control. (That is, it worked well during normal operation but was very much amplified during the conditions prior to the accident.) The accident happened when a small amount of extra reactivity was added to a region that already had an extra large power distribution and extra large positive void coefficient.

Remember that the "problem" of the extra reactivity due to the graphite displacers was known but not thought to be very important, since the reactor was not supposed to be anywhere near the state it was in during the accident.

Was steam being generated at the bottom of the reactor rather than at the top (how?), causing the positive void coefficient to become apparent here but not yet in the rest of the reactor? Is it because the xenon poisoning was concentrated in the center of the reactor (thus the slight decrease in flux shown in graph "a" at center as compared to 80% top or bottom), so the little bit of extra reactivity caused by the water displacement caused runaway reactivity due to the xenon being burned off?

Basically yes, that's what the aforementioned IAEA report says.

Quote:

Originally Posted by IAEA report

This situation in extreme conditions can be highly
unstable, because small spatial redistributions of reactivity can cause large spatial
redistributions of the power. One manifestation of this decoupling of the core is that
just prior to the accident the chain reactions in the upper and lower halves of the reactor
were proceeding almost independently, a situation that was exacerbated by heavy
xenon poisoning in the intervening central region. When control and safety rods were
inserted from fully withdrawn positions under these circumstances, the positive
scram effect discussed earlier could cause the lower part of the core to become
supercritical and the neutron distribution to shift quickly downwards irrespective of
the distribution just prior to rod insertion. Under the conditions of the accident, the
shift in power distribution resulting from the positive scram could be substantial.

Of course the flux does not "equalize" when there's a positive reactivity feedback loop.
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So on a related note, I guess the runaway reaction was just too fast and powerful for the negative temperature coefficient to have any effect? Is it a good check/balance on reactivity when everything's working properly, but it can't overcome unstable conditions?
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Yes I understand the positive void coefficient. It's not about temperature so much as about steam vs water. Water is a weak neutron absorber, and when it's used only as a coolant but not as a moderator (I assume you need a lot more of it to act as a moderator than you find in an RBMK reactor), if it boils the density goes down and thus the neutron absorption goes down, leading to an increase in reactivity and power. That's why it's called positive *void* where void means essentially a steam bubble, or air.

What I'm talking about however is the negative temperature coefficient, which is different. That's simply the process where as the fuel gets hotter, reactivity goes down due to some sort of doppler effect. This is how you can, apparently, increase the output of a reactor simply by increasing the water flow. More flow means cooler water means more reactivity. So in the case of a nuclear submarine, for instance, going from half throttle to full throttle may not require any change in control rod position since the cooler water inflow will by itself increase the reactivity and power.

At Chernobyl, I'm assuming the excursion happened either too quickly for the negative temperature coefficient to matter, or its overall effect was too weak in the face of the runaway reaction.
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The neutron flux and thereby the reactor power increased very fast. Due to the thermal inertia of the fuel and the small value of the fuel temperature coefficient the Doppler effect could not break the power excursion.

At Chernobyl, I'm assuming the excursion happened either too quickly for the negative temperature coefficient to matter, or its overall effect was too weak in the face of the runaway reaction.

OK, I see what you mean. The ENS article indeed says exactly that.

Here is an article about the negative fuel temperature coefficient due to Doppler broadening in nuclear reactors. It says the effect is rapid / almost instantaneous but not very large. "In PWRs, the Doppler coefficient can range, for example, from -5 pcm/K to -2 pcm/K." That's small, and it's smaller when the fuel is hotter.
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